Give the recursive definition for fn 2n n 123 answer choic

Give the recursive definition for f(n) = 2n, n = {1,2,3...}

answer choices :

f(n) = 2n, f(1) = 1

f(n) = 2f(n – 1), f(1) = 2

an = 2n + 2, a1 = 2

an = 2an + 1, a1 = 2

Solution

f(n) = 2n , n = 1,2,3.....

f(1) = 2, f(2) = 4, f(3) = 6,....

f(n) = 2n, f(n+1) = 2n+2

Hence recurrence relation would be

a_n = a_n-1+2, a1 = 2

Or f(n) = 2f(n-1) +2

         = 2{f(n-1) +1}